Lemma 2.3 ([1]})
Suppose \(\alpha _1,\alpha _2>0\)  and \((u,v)\in H^1(\mathbb {R}^4,\mathbb {R}^2)\)  is a nonnegative solution of (REF )-(REF ) with \(2<p<4\) , then \(u>0\)  implies \(\lambda _1>0\) ; \(v>0\)  implies \(\lambda _2>0\) .

